Who killed Asaq Mohammed? His uncle watched him die. Soon after the United States started bombing Afghanistan last autumn the small boy, just under two years old, fled his home on the back of a donkey with his parents and other family members.

For four days they travelled across mountains on snow-covered tracks. At night their only protection against the cold was a handful of blankets. They had no tents.

After three years of drought everyone was already weak with hunger before they set off from the village of Ghorambay in western Afghanistan. The long trek was too much for the most vulnerable. When they reached the town of Owbeh exhausted, Asaq and his six-month-old brother, Abdul Rahman, did not have the strength to recover. Their short lives slipped away.

Seyd Mohammed believes his two nephews would still be alive if they had not been forced to flee. "We were hopeful they wouldn't have died if we had stayed here", he says sadly as he stands outside his home.

With the bombing over, the villagers returned to Ghorambay to pick up the pieces of their broken lives. Like every other house in the small settlement beside a main road, Seyd Mohammed's has a roof made of dried grass spread over a light frame.

As the famine grew last year, people became so desperate for cash to buy food that they took down the roof's original timbers to sell in the nearest town. Next to go were the window frames. Now Seyd Mohammed's house resembles a prison, with rows of small branches propped up in every window like the bars of a cell.

His nephews' deaths can be blamed on drought, poverty, cold, the Taliban, or the Americans, or a combination of some or all of these factors. Sorting them out is not easy. Yet it has relevance in any attempt to calculate the human cost of the US air strikes on Afghanistan.

The direct victims of American bombs and missiles have commanded most political and media attention, though no one is certain how many even of these there were.

A Guardian report in February estimated these casualties at between 1,300 and 8,000 deaths. A Guardian investigation into the "indirect victims" now confirms the belief of many aid agencies that they exceeded the number who died of direct hits.

As many as 20,000 Afghans may have lost their lives as an indirect consequence of the US intervention. They too belong in any tally of the dead.

The bombing had three main effects on the humanitarian situation. It caused massive dislocation by prompting hundreds of thousands of Afghans to flee from their homes.

It stopped aid supplies to drought victims who depended on emergency relief. It provoked an upsurge in fighting and turned a military stalemate into one of chaotic fluidity, leading yet more people to flee.

Counting these victims with accuracy is impossible. As Muslims, Afghans bury their dead within 24 hours and the graves of those who died in the mountains as they fled their homes are only known to their closest relatives.

No one has the time to interview survivors or check their stories. The only way to reach even an estimated figure is by extrapolation and intelligent guesswork.

First, dislocation. Just under a quarter of a million of Afghans fled to Iran and Pakistan after September 11 when it became clear the US would attack. This was no mean achievement, which involved paying smugglers or bribing border guards. Both states had closed their frontiers to Afghans.

In spite of these restrictions the UN refugee agency, the UNHCR, estimated that around 160,000 Afghans crossed into Pakistan by December, often secretly in small groups.

The number reaching the Iranian border is harder to estimate but Iranian officials interviewed by the Guardian in Zahedan in south-eastern Iran talked of 60,000 Afghans crossing in the first month after the bombing. Another 9,000 remained in camps on the Afghan side of the border.

In both cases, these refugees received reasonable amounts of aid once they arrived, either in established refugee/immigrant communities or officially aided camps.

The journey was the problem. An unknown number died on the way. Refugees intending to cross the border tended to be better-off people who knew they would have to pay and brought the funds to do it.

Those who fled within Afghanistan faced different problems. Alan Kresko, acting assistant secretary of the US state department's bureau of population, migration and refugees estimated that 150,000 people were displaced. Others put the figure higher.

The UNHCR estimated that 900,000 were already displaced inside Afghanistan before September 11. In March more than a million were still displaced. Subtracting those who went home to try to take advantage of the spring rains, this still leaves a minimum of 200,000 and possibly more who fled their homes but remained in Afghanistan after September 11.

The luckiest of these internally displaced people (IDPs) moved to relatives near their homes. This was the case for many in the western city of Herat who escaped to villages only a few kilometres away.

There they continued to have shelter and adequate supplies of food. For them the main problem was trauma.

"The bombing was very severe. They mainly hit military targets but the force of the explosions was so intense. It was terrible for children and people with heart problems. My children used to rush to me, I could feel their hearts pounding like a little bird in your hand", said Gholam Rassoul, a driver in Herat.

The group most in danger were those who moved to areas of hunger and cold where they were at greater risk than if they had stayed at home.

In the words of Kate Stearman, head of communications at the British branch of Care International, "After September 11 there was widespread panic in Afghanistan with soaring food prices and mass flight from cities... The bombing and the deteriorating security situation meant huge and largely unrecorded population movements. While the expected one million-plus refugees in Pakistan did not appear, this in itself was worrying because it indicated that many more were trapped inside Afghanistan, their situation unknown".

In Qala-i-Nau, the capital of Badghis, one of the provinces most affected by three years of drought, US bombing caused hundreds to flee from the town to villages where people were closer to starvation than urban-dwellers.

Villagers had no chance to feed the newcomers, Faisal Danesh, a worker for the charity World Vision, told the Guardian. The bombing disrupted aid supplies, prompted expatriate aid workers to pull out of Afghanistan, and stopped Afghan staff from giving aid and medical services in IDP camps, thereby exacerbating their plight.

"For two weeks our Afghan health educators did not travel to the camp because of insecurity caused by the bombing. We had had to leave much earlier", says Dr David Hercot of Medecins du Monde, which works in the sprawling Maslakh camp on the edge of Herat.

No one has exact figures on how much aid was lost as a result of the disruption caused by the bombing. In October national deliveries were estimated to have gone down by 40%.

The main food-deliverer, the World Food Programme, redoubled its efforts as the security situation improved and lorry drivers agreed to take loads back into Afghanistan in November and December. But it remained hard to distribute it to camps and villages.

Before September 11 Afghanistan was already on a lifeline, and for three months we cut the line. Or to put it more starkly: Before September 11, Afghanistan had one of the highest infant mortality rates in the world and one of the lowest rates of overall life expectancy. "Interrupting most of the country's international aid programs for three months only made matters worse," as one western human rights analyst puts it.

"From mid-September to mid-December", he adds "it is possible to say that in areas with already high levels of death from malnutrition and exposure there were likely increases in mortality rates." Such places included central, northern, and western Afghanistan.

"What these increases amount to, no one can say but the fact there were increases is not really in dispute."

The third effect of the bombing was to heighten instability by provoking the Taliban. Until September 11 the Afghan civil war had been stalemated for almost three years. Except in parts of the central region near Bamiyan, the front lines had not moved significantly.

Drought aid moved in to Taliban areas or those controlled by the opposition Northern Alliance with relatively little difficulty. There were shortages but this was because western governments failed to respond to UN appeals for aid to Afghanistan. The aid that was given managed to get through.

For rural Afghans the fact that most cities were controlled by the Taliban was of marginal relevance. They barely saw the Pashtun fundamentalists. In the Tajik village of Kondolan in drought-affected Badghis, for example, rural women did not wear the burka. It was not part of local custom and the Taliban never came to enforce it.

The Taliban ban on girls' education also did not have an effect. "We have had no school of any kind for 25 years", Mirza Behbut, a local farmer, said.

The US intervention ended a military and political stalemate. Deprived of food as American planes targeted their own supply convoys, the Taliban began to steal aid meant for drought victims.

"Before September, the Taliban never looted. They were helped by Pakistan and some Arab countries. After September they faced difficulties in getting their own food," said Faisal Danesh of World Vision. "It made a big difference when the expats left. We would not have had such a big crisis if they had stayed."

World Vision did not have an office in Qala-i-Nau at the time, but Mr Danesh says the Norwegian People's Organisation and the Danish Committee for Aid to Afghan Refugees, which were the main agencies in the region before the bombing, had seeds and grain looted from their warehouses by Taliban militias.

The onset of the bombing raised political tensions to danger level. In Ghorambay, the village where Seyd Mohammed and his small nephews lived, the mojahedin appeared and handed out guns, urging villagers to ambush passing Taliban convoys.

Acting on an informer's tip, theTaliban then raided the village for guns. They found nothing but took five villagers away for torture. Frightened that the detained men would confess (which they did), the remaining villagers fled into the mountains that night on the trek that led the two toddlers to their death.

The best starting point for calculating the number of indirect casualties from America's bombs and missiles is the death rates at IDP camps. The Guardian spent several days in western Afghanistan, the centre of the drought-affected region.

In Herat Medecins du Monde showed the Guardian itemised records from Maslakh camp of named people with the cause of death listed. These were compiled by 15 Afghan health educators who regularly visit the IDPs to check their medical condition.

Each educator concentrates on a small section of the sprawling camp. Some educators are women so that they can win the trust of the female IDPs.

Medecins du Monde found the death total in Maslakh camp averaged 145 per month between September and December last year, almost double the total of 79 for February this year, a clear sign that things were worse during the bombing period.

The total of 580 deaths from September to December was compiled in the two main areas of the camp. They had an estimated population of 80,000. (A survey in February this year found that earlier camp estimates of 350,000 were inflated.) This produces a death rate of 1.8 per 1,000 per month.

"We didn't have educators in Maslakh Three, the area where new arrivals came after September 11. They lived in tents rather than brick shelters. We think their death toll could be higher," Dr David Hercot told the Guardian.

At three smaller IDP camps in other parts of Afghanistan death rates were above those at Maslakh, although statistics appear to have been compiled less strictly (see graphic).

At Dehdadi south of Mazar-i-Sharif which sheltered 15,000 people 230 people died between September 11 when aid stopped and January 11, Stephan Goetghebuer of Medecins sans Frontieres told Time Asia. This is a rate of around 4 per 1,000 per month.

At Baghe Sherkat and Amirabad camps near Kunduz the WHO reported that 164 people out of a population of 25,000 IDPs died of hunger, cold, and disease in a period of roughly two months. This is a rate of 3 per 1,000 per month.

The death rate was lower at Dasht-e-Arzana camp outside Mazar-i-Sharif. Officials told Lynne O'Donnell of the newspaper the Australian that people were dying in early December at the rate of around 1.15 per 1,000 per month in a population of 21,000.

At Nasaji camp in Balkh province with 14,500 IDPs 19 people died of malnutrition and exposure in November, a rate of 1.3 per 1,000 for that month.

Taking into account the difference in size among the camps the average mortality rate comes to 2 per 1,000 per month. The camps covered by these figures contained about three-quarters of the total IDP population of around 200,000 in camps.

Extrapolating, this produces an average of 400 deaths in the camps every month, or 1,600 from September to the end of December. It is hard to be sure that whether the one million IDPs outside camps would have had comparable death rates. If they did, the number of deaths would be 8,000 between September and December last year.

The Project for Defence Alternatives of the Massachusetts-based Commonwealth Institute takes a critical view of the US intervention. Carl Conetta, its director, who made the first attempt in January to calculate the intervention's humanitarian costs, argued that the million IDPs outside camps were at severe risk.

"A worst case may be represented by 2,000 families in the central highlands who were suffering mortality rates in excess of 7.5 people per 1,000 per month", he wrote in a report available at www.comw.org.

The best case would be those people interviewed by the Guardian near Herat who fled to lowland villages nearby. Beside the refugees and IDPs, five million very poor Afghans remained at home during the bombing but had drought relief aid deliveries disrupted.

Assuming the mortality rates for these five million people were the same as those in the IDP camps would produce an additional number of avoidable deaths from September to December of 40,000.

This is a maximum assumption. Adding this figure to the 1,600 estimated deaths in the camps and the 8,000 deaths of IDPs outside the camps, the top figure would be 49,600.

Mr Conetta came to the preliminary conclusion that numbers of indirect deaths above 20,000 were unlikely, mainly because of a lack of specific reports or evidence.

How many of the post-September 11 deaths would have occurred anyway, even if there had been no bombing, given that so many Afghans were weakened by drought?

All one can say is that the bombing caused a decline in aid deliveries to Afghanistan in October of 40%. Although it picked up sharply thereafter, distribution within the country was much harder than it had been before the bombing.

Taking 40% as a benchmark, one would conclude that the US intervention caused around 40% of the maximum number of assumed deaths. This amounts to 19,840 people.

Even if one halves the estimated percentage to 20%, a rough total of 10,000 will have died "indirectly" because of the US campaign. The range of estimates is broad but it clearly exceeds the scale of for those killed by bombs.

No one will ever know the true figure, and as time goes on, the chances of reaching even a narrower estimate of the scale of death are more likely to recede than grow.

The nameless graves on Afghanistan's hillsides, in patches of the desert, and obscure corners of IDP camps will slowly be forgotten.